Phase Transitions in the Diluted Two-Dimensional Potts Model with the Number of Spin States q = 3 on a Square Lattice

Physics of the Solid State - The phase transitions in the two-dimensional diluted Potts model with the number of spin states q = 3 are studied by computer simulation method. The systems...     

Study of the Two-Dimensional Anisotropic Ising Model with Competing Interactions in the Region of a Transition from the Ferromagnetic to Paramagnetic State

Journal of Experimental and Theoretical Physics - The two-dimensional anisotropic Ising model with competing interactions in the region of a transition from the ferromagnetic to paramagnetic phase...     

Effect of Exchange Interaction Constants on the Magnetization Reversal in a Hard/Soft Magnetic Bilayer Model

Journal of Experimental and Theoretical Physics - A model is developed to study a hard/soft magnetic bilayer in an external magnetic field by the Monte Carlo method. The influence of the constants...     

Investigation of the thermodynamic properties and phase transitions in a strongly diluted three-vertex antiferromagnetic Potts model by the Monte Carlo method

Physics of the Solid State - The thermodynamic properties and phase transitions in a two-dimensional strongly diluted threevertex antiferromagnetic Potts model on a triangular lattice have been...     

Computer simulation of the frustrated antiferromagnetic Heisenberg model on a layered triangle lattice

Critical properties of the 3D frustrated Heisenberg model on a triangle latticeare investigated using a replica Monte-Carlo method that considers the interaction between next nearest neighbors. Static magnetic and chiral critical indices for heat capacity α, susceptibility γ, γ _k , magnetization β, β _k , and correlation radius ν are calculated using the theory of finite-size scaling.     

Investigation of the critical properties of the frustrated Heisenberg model on a triangular lattice by the Monte Carlo method

The critical properties of the 3D frustrated antiferromagnetic Heisenberg model on a triangular lattice have been investigated by the replica Monte Carlo method. All main magnetic and chiral critical indices were calculated using the finite-size scaling theory. It is found that the class of universality of the critical behavior of the model studied depends on the type of interplane exchange interaction.     

Dynamic critical behavior of the Heisenberg model with strong easy plane anisotropy

The dynamic critical behavior of the Heisenberg model with a strong anisotropy of the exchange constant in the z direction is investigated. The main features of the time evolution of this model are revealed. The static and dynamic critical behavior of planar magnetic models is shown to be described well by the Heisenberg model with strong easy plane anisotropy.     

Phase transitions and critical phenomena in a three-dimensional site-diluted Potts model

The phase transitions and critical phenomena in the three-dimensional (3D) site-diluted q-state Potts models on a simple cubic lattice are explored. We systematically study the phase transitions of the models for q=3 and q=4 on the basis of Wolff high-effective algorithm by the Monte–Carlo (MC) method. The calculations are carried out for systems with periodic boundary conditions and spin concentrations p=1.00–0.65. It is shown that introducing of weak disorder (p∼0.95) into the system is sufficient to change the first order phase transition into a second order one for the 3D 3-state Potts model, while for the 3D 4-state Potts model, such a phase transformation occurs when introducing strong disorder (p∼0.65). Results for 3D pure 3-state and 4-state Potts models (p=1.00) agree with conclusions of mean field theory. The static critical exponents of the specific heat α, susceptibility γ, magnetization β, and the exponent of the correlation radius ν are calculated for the samples on the basis of finite-size scaling theory.     

Phase transitions in the two-dimensional ferro- and antiferromagnetic potts models on a triangular lattice

The phase transitions in the two-dimensional ferro- and antiferromagnetic Potts models with q = 3 states of spin on a triangular lattice are studied using cluster algorithms and the classical Monte Carlo method. Systems with linear sizes L = 20–120 are considered. The method of fourth-order Binder cumulants and histogram analysis are used to discover that a second-order phase transition occurs in the ferromagnetic Potts model and a first-order phase transition takes place in the antiferromagnetic Potts model. The static critical indices of heat capacity (α), magnetic susceptibility (γ), magnetization (β), and correlation radius index (ν) are calculated for the ferromagnetic Potts model using the finite-size scaling theory.     

Statical critical properties of gadolinium models

Microscopic models of real ferromagnetic gadolinium are proposed, and their critical properties are studied by the Monte Carlo method. The critical exponents α (heat capacity), γ (susceptibility), and β (magnetization) are calculated. The α, β, and γ exponents are determined by the approximation of the data on the basis of traditional power functions and in the framework of the finite-size scaling theory. It is revealed that the critical behavior of gadolinium is affected by the dipole-dipole interactions. It is shown that the Monte Carlo method is a powerful tool for investigations into the critical properties of complex models in which two types of weak relativistic interactions are jointly taken into account against the background of each of these interactions.